David Cameron said he was "deeply saddened" by the death of a British national in the bomb attack on a popular shrine.
The woman, a resident of Hong Kong, was confirmed by the Foreign Office to be among at least 20 victims of the blast in Thailand's capital Bangkok.
"Deeply saddened to hear a British national was killed in the horrific Bangkok bombing," the Prime Minister said in a statement posted on Twitter.
"My thoughts are with her family and all those affected."
Thai authorities are searching for a man caught on security cameras leaving behind a rucksack at the popular attraction, which is in an area well-used by foreign visitors.
More than 100 were injured by the blast.
Foreign Secretary Philip Hammond said: "Foreign Office officials are in close contact with the Thai authorities and have offered UK assistance in the investigation of this abhorrent act.
"British nationals in Thailand should check the Foreign Office website for the latest travel advice."
Hong Kong has raised its travel alert to red and advised its citizens to avoid non-essential trips to Bangkok but the British Government has not taken similar action.
Travel advice issued by the Foreign and Commonwealth Office (FCO) cautions people to "monitor news reports, follow the advice of local authorities and take extra care".
Five of the victims have so far been identified as Thais, four as Chinese - including two from Hong Kong - two from Malaysia and one from Singapore.
No-one has yet claimed responsibility for the bombing, which bears none of the hallmarks of the Muslim separatists who have been fighting a long insurgency in the south of the country and who have not tended to target the capital.